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I am currently designing an extremely simple Keplerian telescope and am confused as to why many explanations say that the objective lens and eyepiece lens are positioned a distance of the sum of their focal points away (fobjective+feyepiece). As pictured in the figure below, when the two lenses have positioned a distance of the sum of their focal points away, the light rays that ultimately hit the eye will be parallel; meaning that they will never converge and therefore the eye will never be able to piece together an image. Or the other way I think about it is that the object distance of the eyepiece lens is at its own focal point, which as we know, won't form an image.

Keplerian Telescope Ray Diagram

From my belief, if the objective lens is positioned just where fobjective is inside feyepiece, this will create an extremely magnified image and will be the perfect alignment of a telescope. So should I align the focal points as just described above, or should they be aligned as shown in the picture and described by many books? If so, why?

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Parallel rays entering a relaxed eye with normal vision will be focused by the cornea and lens of the eye to form an image on the retina. As far as the eye is concerned, the parallel rays coming from a Keplerian telescope are entirely equivalent to the (nearly) parallel rays coming from a distant object. If one relaxes one's eye (and one's far point is sufficiently far away), one will be able to see the image through the Keplerian telescope clearly.

The real power (pun intended) of the Keplerian telescope is that it increases the angle these rays make with the optical axis. This means that an object that would have subtended (for example) 1 arcminute and just barely have been resolvable by the naked eye might now subtend 20 arcminutes and be readily resolvable.

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